On surfaces with p_g=2q-3

TL;DR

This paper classifies minimal complex surfaces of general type with specific invariants, providing bounds on their invariants and describing their Albanese maps, advancing understanding of their geometric structure.

Contribution

It offers a complete classification for surfaces with a fibration onto a curve of genus >=2 and establishes new inequalities relating invariants of these surfaces.

Findings

K^2=8χ for surfaces with a fibration onto a genus >=2 curve

Proved K^2>=7χ generally, with stronger bounds under certain conditions

Described the Albanese map of these surfaces

Abstract

We study minimal complex surfaces S of general type with q(S)=q and p_g(S)=2q-3, q>= 5. We give a complete classification in case that S has a fibration onto a curve of genus >=2. For these surfaces K^2=8\chi. In general we prove that K^2>=7\chi-1 and that the stronger inequality K^2\ge 8\chi holds under extra assumptions (e.g., if the canonical system has no fixed part or the canonical map has even degree). We also describe the Albanese map of S.